A hierarchical latent variable model for data visualization

Christopher M. Bishop, Michael E. Tipping

    Research output: Contribution to journalArticlepeer-review


    Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.
    Original languageEnglish
    Pages (from-to)281-293
    Number of pages13
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Issue number3
    Publication statusPublished - Mar 1998

    Bibliographical note

    Copyright of Institute of Electrical and Electronics Engineers (IEEE)


    • Latent variables
    • data visualization
    • EM algorithm
    • hierarchical mixture model
    • density estimation
    • principal component analysis
    • factor analysis
    • maximum likelihood
    • clustering
    • statistics.


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